75.16.10 problem 483

Internal problem ID [16983]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 483
Date solved : Tuesday, January 28, 2025 at 09:44:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right )-\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)+y(x)=sin(x)-cos(x),y(x), singsol=all)
 

\[ y = \frac {\left (-x +2 c_{1} -1\right ) \cos \left (x \right )}{2}-\frac {\sin \left (x \right ) \left (x -2 c_{2} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.267 (sec). Leaf size: 62

DSolve[D[y[x],{x,2}]+y[x]==Sin[x]-Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x) \int _1^x(\cos (K[1])-\sin (K[1])) \sin (K[1])dK[1]+\sin (x) \int _1^x\cos (K[2]) (\sin (K[2])-\cos (K[2]))dK[2]+c_1 \cos (x)+c_2 \sin (x) \]